Volunteering in public goods games

by Christoph Hauert, Version 1.0, April 2002.

The evolution of cooperation among non-related individuals is one of the
fundamental problems in biology and social sciences. Reciprocal altruism
fails to provide a solution if interactions are not repeated often
enough or groups are too large. Punishment and reward can be very effective but
require that defectors can be traced and identified. Here we present a simple
but effective mechanism operating under full anonymity. Optional participation
can foil exploiters and overcome the social dilemma. In voluntary public goods
interactions, cooperators and defectors will coexist.
We show that this result holds under very diverse assumptions on population
structure and adaptation mechanisms. Thus, voluntary participation offers an escape
hatch out of some social traps. Cooperation can subsist in sizeable groups even
if interactions are not repeated, defectors remain anonymous, players have no
memory and assortement is purely random.

The following pages are designed as additional material to these articles and
meant as an interactive tutorial taking advantage of Java applets to visualize and
experiment with the system's dynamics for parameter settings of your choice.

Public goods games

In a typical setup in experimental economics an experimenter endows e.g. six
players with $10 each. The players are then offered to invest their money into
a common pool knowing that the experimeter will triple the amount in the pool
and distribute it equally among all participants irrespective of their
contributions. If all players cooperate and contribute their $10, they
will end up with $30 each. However, each player faces the temptation to
defect and to free-ride on the other player's contributions since each
invested dollar yields only a return of 50 cents to the investor. Therefore
the 'rational' and dominating solution is to defect and invest nothing.
Consequentially, groups of rational players will forego the public good
and are thus unable to increase their initial endowment. This results in
a deadlock of mutual defection and economic stalemate.

Such public goods interactions are abundant in human and animal societies.
Consider for example predator inspection behavior, alarm calls and group
defense as well as health insurrance, public transportation, the fight against
crime or environmental issues, to name only a few.

Voluntary participation

Most theoretical and experimental studies on public goods games or the related
prisoner's dilemma have tacitly built on the fact that the participants are
actually prisoners, i.e. they are trapped in the dilemma. In nature, however,
animals and humans often have, at least to a certain extend, the freedom to
decide whether to participate in a public enterprise.

For this reason we extend the public goods game to allow for voluntary
participation. Individuals unwilling to participate are termed loners. They
prefer autarky and rather rely on some small but fixed payoff. The loner
strategy is thus risk averse. But, the option to withdraw from social or
economic enterprises efficiently avoids deadlocks in states of mutual
defection and economic stalemate.

In the following we thus consider three strategical types: (i) cooperators
and (ii) defectors both willing to join the public goods game, with different
intentions though, and (iii) loners that refuse to participate. These strategies
lead to a rock-scissors-paper dynamics with cyclic dominance: if cooperators
abound, they can be exploited by defectors, but if defectors prevail it is best
to abstain and if no one participates, small groups can form and it pays to
return to cooperation.

Population structure

In order to model spatially extended systems, we consider players arranged on
regular lattices. They interact only with their nearest neighbors.

Acknowledgements

For the development of these pages help and advice of the following two people
was of particular importance: First, my thanks go to Karl Sigmund for helpful
comments on the game theoretical parts and second, my thanks go to Urs Bill
for introducing me into the Java language and for his patience and competence in
answering my many technical questions.
Financial support of the Swiss National Science Foundation
is gratefully acknowledged.